1. 1
   $\vec{a} = \begin{pmatrix} 3 \\ -2 \end{pmatrix}$ and $\vec{b} = \begin{pmatrix} -1 \\ 4 \end{pmatrix}$.

   (a)

   What is $\vec{a} + \vec{b}$?

   [1 mark]

   • A$\begin{pmatrix} 2 \\ -6 \end{pmatrix}$
   • B$\begin{pmatrix} 4 \\ -6 \end{pmatrix}$
   • C$\begin{pmatrix} -2 \\ -2 \end{pmatrix}$
   • D$\begin{pmatrix} 2 \\ 2 \end{pmatrix}$

   (b)

   What is $2\vec{a} - \vec{b}$?

   [1 mark]

   • A$\begin{pmatrix} 5 \\ 0 \end{pmatrix}$
   • B$\begin{pmatrix} 7 \\ -8 \end{pmatrix}$
   • C$\begin{pmatrix} 7 \\ 0 \end{pmatrix}$
   • D$\begin{pmatrix} 5 \\ -8 \end{pmatrix}$

   (c)

   What is the magnitude of $\vec{a}$, to 3 significant figures?

   [1 mark]

   • A1.00
   • B5.00
   • C3.61
   • D13.0

   Total for question 1: 3 marks

2. 2
   In triangle OAB, $\vec{OA} = \vec{a}$ and $\vec{OB} = \vec{b}$. M is the midpoint of AB.

   (a)

   Express vector AB in terms of $\vec{a}$ and $\vec{b}$.

   [2 marks]

   (b)

   Express vector OM in terms of $\vec{a}$ and $\vec{b}$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In triangle OPQ, $\vec{OP} = \vec{p}$ and $\vec{OQ} = \vec{q}$. R is the point on PQ such that PR:RQ = 2:1.

   (a)

   Express vector PQ in terms of $\vec{p}$ and $\vec{q}$.

   [3 marks]

   (b)

   Express vector OR in terms of $\vec{p}$ and $\vec{q}$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   OABC is a parallelogram, where $\vec{OA} = \vec{a}$ and $\vec{OC} = \vec{c}$. M is the midpoint of OC, and N is the midpoint of AB.

   (a)

   Express vector OB in terms of $\vec{a}$ and $\vec{c}$.

   [4 marks]

   (b)

   Express vector ON in terms of $\vec{a}$ and $\vec{c}$.

   [4 marks]

   (c)

   Prove that MN is parallel to OA.

   [5 marks]

   Total for question 4: 13 marks

End of questions